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Blackjack basic strategy makes the assumption that the player is playing independently, with one person's decision to hit/stand having no affect on another player's decision to hit/stand. If the results of every single hand were independent from each other, then there would be no way to improve upon basic strategy and gain a positive expected return.

Blackjack hands, however, are not independent events. Card counting takes advantage of the fact that the next hand is not independent of previous hands, due to the limited number of decks in the shoe.

A few days ago, I realized that there might be another way to gain an advantage by using the fact that the results for individual players during a single round are not independent of each other.

For example, most players will win when the dealer has a weak hand, and most players will lose when the dealer has a strong hand. Also, one player's cards reveal information about the probable outcome for both other player's hands and the dealer's hands for that particular round (even when there is a continuous shuffle machine being used).

If player A and player B have expected returns that are not independent of each other, is there a way for them to work together to alter their strategy in a way as to decrease the house edge?

Because of the common use of a shoe, many Blackjack tables, several hands are not independent. Only when the deal is from a freshly shuffled deck is the hand independent of the prior hand.
–
aramisMay 24 '13 at 8:23

5 Answers
5

In a loose sense, players can collaborate by signaling each other their hole card when the deal is one up one down. this allows far better optimization by almost doubling the known number of cards for the sharp who counts. Especially true if one or more goes for small bets and lots of draws.

The more cards are known to a sharp, the better he's able to account the odds.

Note that signaling, if caught, is potentially grounds for removal from the facility and forfeiture of any chips.

I think that if one was betting table minimum and the other max bet x 2 or or close to it, with the small player in front of the gorilla, taking advantage of the count if they know it, and trying to hole card the dealer, they could make a decent living. The ideal situation would be the gorilla playing 5/6 with the small player at 4. The small player would try to act like a hunch or amatur player.

This is going to work at only the lowest of venues as any decent surveillance operator is going to see right through it even if they try to cap black with green or red, and have more than one stooge to be the small player.

This sounds really interesting, would you mind explaining a bit more? It's pretty jargon-y as is and I don't know enough to understand it.
–
GregorFeb 3 '14 at 23:49

The small player bets table minimum. The big player "gorilla" bets table max x 2 hands. The gorilla signals the small player how to play his hand, tapping his cigarette or riffling his chips, depending on what he wants him to do. Don't try this as the wild deviations from basic strategy will bring heat from the pit and/or surveillance. By capping a bet I mean putting a smaller denomination on top of a larger one to disguise the amount of the bet from surveillance. They are busy watching for big chips $100/500/1000.
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eagle eyesFeb 4 '14 at 0:22

By changing out the stooge, I mean one time he is uncle Ho from the old country, next time a ditzy young female. Those kind of players are not expected to play perfect basic strategy. That way surveillance or the pit does not make the connection between the two players. I hope this has removed some of the confusion from my answer.
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eagle eyesFeb 4 '14 at 0:56

By hole carding I mean trying to get a look at the dealers down card. The best place to do this is from third base when it comes out of the shoe or from the third or fourth betting spots when the dealer uses the peek to see if he has an ace. I hope this has removed some of the confusion from my answer.
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eagle eyesFeb 4 '14 at 1:07

Looking at it purely mathematically, given that there is no hidden information, there is no difference between a "team" of blackjack players playing as you describe, and one player playing multiple hands. So why don't card counters typically recommend playing multiple hands?

Card counting works because the player's winrate is dependent on the distribution of cards remaining in the deck. Most of a card counter's edge comes from adjusting their bet before the hand is dealt. Playing multiple hands means getting less information between placing bets, not more.

It is true that one player could alter their playing strategy based on the results of another player's hits, but there are some serious problems:

If you're talking about the information gained from the dealer's hole card, this is unaffected by your decision to "collude"

The times when the probabilities seriously change based on the turn of one or two cards, the shoe is probably marginal so you should be betting near the lower end of your spread anyway

Flagrantly altering your strategy based on a card count is so obvious a card counting flag that even card counters will often advise against doing it, especially given that the edge will be marginal

After looking at other answers, I feel it's worth mentioning in a footnote that I stuck to the math because that was what OP was really asking. There are reasons (like outright cheating) that it might be advantageous to have partners, but not anything like what was described in the question.
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Chad MillerFeb 4 '14 at 6:29

And in one of his "Bringing Down the House" series of books, Ben Mezrich talked about how a skilled player would insert the "cut" (and shown) card at exactly a particular place in the deck.

Depending on whether they wanted the dealer to draw or "miss" the card, the players would either draw or stand on the round that the particular cut card was dealt. That gave the players a ONE HAND advantage that was apparently enough to more than cancel out the house advantage.

When you break it down statistically and you're dealing with someone who can card-count, ace-track, shuffle-track, and perform / maintain a running tally of any other relevant factor in the game, it will always be to their advantage to be in control of as many hands as possible.

Playing on a team allows for a single mindset or approach to be taken towards every position on the table. Because a professional card counter is very 'informed' of the state of the remaining deck, they want to be able to manipulate the way those cards are dealt to the players as much as possible. This is why they would want to play every position on the table, as long as it doesn't interfere with their ability to count. Because of casino policies this may not be possible without having teammates who are under your 'command' and play the hands that you are not able to safely play without being asked to leave.